Normal state specific heat of a core-shell aluminum-alumina metamaterial composite with enhanced $T_c$

The metamaterial approach to dielectric response engineering for enhancing the transition temperature, $T_c$, of a superconductor has been demonstrated in several recent reports. One example of this effect is ${\mathrm{Al}}_2{\mathrm{O}}_3$ coated aluminum nanoparticles that form an epsilon near zero (ENZ) core-shell metamaterial superconductor with a $T_c$ that is nearly three times that of pure aluminum. Since the $T_c$ of a conventional low temperature superconductor is determined by the Debye temperature and the coupling strength, which is expressed as the product of the single particle density of state (DOS) at the Fermi energy and an attractive electron-electron potential, it is natural to explore these properties to determine whether the attractive potential is responsible for the enhancement. In this report, we present specific heat results obtained from ${\mathrm{Al}}_2{\mathrm{O}}_3$ coated aluminum nanoparticle composite pellets with an enhanced $T_c$ that demonstrate that the Debye temperature and DOS are similar to that of pure aluminum indicating that the source of the $T_c$ enhancement is indeed a modification of the attractive electron-electron interaction.

Figure 1

Field cooled and zero field cooled magnetization vs temperature of the sample in a 10 Oe magnetic field.

Figure 2

Molar heat capacity at constant pressure as a function of temperature for $\mathrm{Al}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ nanoparticles measured both in a copper cup and directly.

Figure 3

Low temperature molar heat capacity at constant pressure as a function of temperature for $\mathrm{Al}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ nanoparticles measured both in a copper cup and directly.

Figure 4

Percent deviation between the measurement of $\mathrm{Al}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ nanoparticles heat capacity made in a copper cup and the direct measurement.

Figure 5

Calculated molar heat capacity at constant pressure as a function of temperature for aluminum metal cores of $\mathrm{Al}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ nanoparticles given different molecular formulas as noted. Measured heat capacity values for aluminum metal are included for reference.